Replacement Ratio
3. Results and Analysis 1. Failure Procedure and Mode
(a) (b) (c)
Figure 3. Photos and sketch of the test: (a) photo of test setup; (b) photo of push-out specimen;
(c) sketch of push-out specimen.
3. Results and Analysis
Appl. Sci.2020,10, 887
With bursting failure, the initial cracks occurred in the middle of the flange or the web. As the load increased, the initial cracks gradually expanded toward the loading and free ends, and some new fine cracks occurred. When the load reached about 80%–90% of the ultimate load, the initial cracks continued expanding and widening, and there were many obvious secondary cracks. As shown in Figure5(taking SRRC-1 as an example), through cracks were present on both the flange and the web sides after failure. This is one of the main features of bursting failure that makes it different from the splitting failure.
(a) (b)
Figure 5.Bursting failure of SRRC-1: (a) web; (b) flange.
It can be seen from SRRC-4 and SRRC-8 specimens that a high lateral stirrup ratio and high cover thickness make the specimen more prone to bursting failure. The reason for this phenomenon is that a high lateral stirrup ratio and high cover thickness are effective in preventing the deformation of concrete and further improving the cracking load of cracks.
3.2. Characteristic of P–S Curves
The loading end slip curve (P-S curve) can be simplified to the model shown in Figure6. Here, The load is divided into two categories, each of them showing basically the same changes, which are divided into three parts: rising, sag, and gentle loads. Type (I) is characterized by a large initial load (65%–75% of the peak load), with a residual load that is slightly lower than the initial load. Type (II) is characterized by a small initial load (40%–65% of the peak load), with a residual load that is slightly higher than the initial load. The P–S curves of the specimens are shown in Figure7.
The following definitions of the characteristic points in Figure6are given:
(1) The initial load Ps: The load when obvious slippage occurred on specimens (point A) (2) The ultimate load Pu: The maximum value of the specimens (point B)
(3) The residual load Pr: The load corresponding to the end of the descending stage (point C)
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(a) (b)
F
Figure 6.P–S curve models of the loading end: (a) Type (I); (b) Type (II).
(a) (b)
FF (d)
(e) (f) Figure 7.Cont.
Appl. Sci.2020,10, 887
(g) (h)
(i) Figure 7.P–S curves of each specimen: (a) SRRC-1; (b) SRRC-2; (c) SRRC-3; (d) SRRC-4; (e) SRRC-5;
(f) SRRC-6; (g) SRRC-7; (h) SRRC-8; (i) SRRC-9.
In this paper, the P–S curves of the loading end are divided into four stages: nonslip, slip-crack, descending, and residual.
(1) OA in Figure6indicates the nonslip stage of the specimens. The key point is the initial bond load point, which determines the length of the section, and the main load is borne by the chemical adhesive force at this section. The composition of the bond stress in the section steel and RAC is similar to in the section steel and ordinary concrete. The bond stress is caused by chemical adhesion and frictional resistance in the article [33].
(2) AB in Figure6indicates the slip-crack stage of the specimens, where the curve is basically a linear relationship and the slope is too large. When loading to 40%–65% of the ultimate load (the load is defined as the initial load Ps, the corresponding bond strength is the average initial bond strength τs), the loading end of the specimen begins to slip and developed rapidly.
(3) The load drops sharply and the specimen has longitudinal through cracks when loading increases to the ultimate load Pu(the corresponding bond strength is the average limited bond strength τu). The reason is that the chemical adhesion of the descending stage is suddenly broken and the friction is not sufficient to support the ultimate load.
(4) The residual mainly depends on the residual load. The P–S curve is basically a horizontal line when the load falls to 50%–70% of the ultimate load (the load is defined as the residual load Pr, the corresponding bond strength is the average residual bond strengthτr). It can be concluded that the determinants of each stage are the characteristic loads.
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3.3. Influence Analysis of Various Factors
The bond strength between the section steel and RAC can be considered to be evenly distributed along the length of the section steel under the push-out test conditions. The average bond strength can be expressed by Equation (1).
τ= P
Le·C (1)
whereτis the average bond stress in MPa;Pis the load in N;Leis the embedded length of section steel in mm; andCis the perimeter of section steel in mm.
3.3.1. Concrete Strength
The bond strength is basically a linear relationship with the tensile strength of RAC, and the bond strength increases with the increase of tensile strength, as shown in Figure8a. Equation (2) [34] was adopted in this study, which reflects the relationship between the tensile strength and compressive strength of RAC.
ft=0.18fcu23 (2)
wherefcuis the compressive strength of RAC;ftis the tensile strength of RAC.
(a) (b)
(c) (d)
Figure 8.Relationship of bond strength and various factors: (a) concrete strength; (b) embedded length;
(c) cover thickness; (d) lateral stirrup ratio.
The relationship between the tensile strength (ft) of RAC and the average bond strength (τ) is obtained by statistical regression, which is fit as Equations (3)–(5).
τs=0.125ft+0.431 (3)
τu=0.511ft+0.549 (4)
Appl. Sci.2020,10, 887
τr=0.567ft−0.097 (5)
3.3.2. Embedded Length
The relative bond strength is defined as the ratio of the average bond strength to the tensile strength (τ/ft), and the relative embedded length is defined as the ratio of the embedded length to the height of the section steel (Le/d). The relationship between the embedded length and the average initial bond strength, the average ultimate bond strength, and the average residual bond strength are shown in the following equations:
τs= (−0.011Le/d+0.440)ft (6) τu= (−0.070Le/d+1.247)ft (7) τr= (−0.041Le/d+0.736)ft (8) As can be seen from Figure8b, the bond stress decreases as the embedded length increases.
The reduction effect of the average initial bond strength is not obvious, and the average ultimate bond strength decreases significantly.
3.3.3. Cover Thickness
The relative cover thickness is calculated from the ratio of the cover thickness to the height of the section steel (Css/d). The cover thickness refers to the distance between the section steel and the outer surface of RAC. The relationship is shown in the following equations:
τs= (1.566Css/d−0.318)ft (9) τu= (0.983Css/d+0.317)ft (10) τr= (0.469Css/d+0.243)ft (11) It can be seen from Figure8c that the average characteristic bond strength obviously increases with the increase of the cover thickness.
3.3.4. Lateral Stirrup Ratio
The effect of the lateral stirrup ratio is similar to that of the cover thickness, which can effectively prevent the lateral deformation of the RAC and delay the cracking time. The equations are as follows.
τs= (2.934ρss−0.206)ft (12) τu= (0.269ρss−0.770)ft (13) τr= (1.556ρss−0.172)ft (14) It can be seen from Figure8d that the average characteristic bond strength increases with the increase of the lateral stirrup ratio, and the average initial bond strength increases obviously. The effect of increasing the ultimate bond strength is poor, indicating that the increase of the lateral stirrup ratio can effectively delay the appearance of the initial crack and increase the cracking load, but the effect on improving the average ultimate bond strength is not significant.
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3.4. Formulas
The characteristic bond load and the average characteristic bond strength of specimens are shown in Table5. The formulas for the average bond stress of the four factors were established by statistical regression analysis. They can be expressed as follows.
τs= (−0.686Css
d +0.020Le
d +2.506ρsv+0.067)ft (15)
τu= (−0.335Css
d +0.015Le
d +0.718ρsv+0.683)ft (16)
τr= (−0.493Css
d +0.006Le
d −0.842ρsv+0.590)ft (17)
whereτsis average initial bond strength;τuis average ultimate bond strength;τris average residual bond strength.
In order to verify the reliability of the formulas, the comparison was performed between the calculation of the formulas and the experiment data from this test, as well as using data from Yin et al. [35], Chen et al. [24], and Chen et al. [36]. The results are shown in Table6.
Table6indicates that the average ultimate bond strength and the average residual bond strength fit well, but the fitting result of the average initial bond strength has a certain error. One of the reasons for this error is the different values of initial load between the man-made and instrument methods.
In addition, Equation (2) by Xiao et al. [34] for the tensile strength of RAC was used in this study, but the rest of the articles adopted ordinary concrete formulas. The tensile strength of RAC under the same compressive strength is higher than in this paper.
Appl. Sci.2020,10, 887
Table5.Resultsofcharacteristicloadandbondstresstests. No.MainAnchoringCondition Ps/KNPu/KNPr/KNτs/MPaτu/MPaτr/MPaReplacement (%)Concrete Strength(MPa)Cover Thickness(mm)Embedded Length(mm)LateralStirrup Ratio(%) SRRC-1100C30557400.22485593240.6331.4260.827 SRRC-2100C30555400.22034662780.7101.6290.972 SRRC-3100C30407400.22044712750.5201.2020.702 SRRC-4100C30707400.25056603831.2881.6840.977 SRRC-5100C40557400.22846734780.7241.7171.219 SRRC-6100C20557400.22424972870.6171.2680.732 SRRC-7100C30557400.253815713320.9721.4570.847 SRRC-8100C30557400.34475774301.1401.4721.097 SRRC-9100C30559400.23007213760.6021.4480.755 Table6.Comparisonofcharacteristicbondstrength. SourceNo.InitialBondStrength Calculated/TestedLimitBondStrength Calculated/TestedResidualBond StrengthCalculated/Tested CalculatedTestedCalculatedTestedCalculatedTested Article
SRRC-10.6300.6330.9961.3201.4260.9260.8270.8271.000 SRRC-20.6000.7100.8451.3441.6290.8250.8920.9720.918 SRRC-30.8330.5201.6021.4751.2021.2280.9930.7021.416 SRRC-40.4971.2880.3861.3111.6840.7790.7510.9770.769 SRRC-50.8290.7241.1441.7361.7171.0111.0871.2190.892 SRRC-60.5070.6170.8221.0631.2680.8380.6650.7320.909 SRRC-70.8480.9720.8721.3821.4570.9490.9000.8471.062 SRRC-81.0651.1400.9341.4441.4720.9810.9731.0970.887 SRRC-90.7310.6021.2131.4421.4480.9960.8530.7551.129 Chenetal.SRRAC-111.4381.6700.8611.7191.9630.8761.2581.4040.896 Chenetal.SRAC-51.3180.9301.4171.8211.5101.2061.2380.9901.251 Yinetal.SRRC-340.8600.5011.7171.2130.9051.3400.8010.4121.944 SRRC-350.8070.3492.3111.1251.1390.9880.7980.6291.269 SRRC-360.3790.4920.7701.0001.0380.9640.5730.6370.899
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